CPhill

a + 14d  = 9a    →  8a   = 14d  →   d = [8/14]a   =  (4/7)a

So

S₃₅  = (35/2) [2a + 34 (4/7) a ]

S₃₅   = (35/2) [ 2a + (136/7)a ]

S₃₅  = (35/2) [ (150/7)a ]

S₃₅ = ( 35/7)(150/2) a  = (5)(75) a   =  375 a

We have

-7  = a₁ + (14)d     → 14d  = -7 - a₁      (1)

210  = (15/2) (2a₁ + 14(d) )      (2)

Sub (1)  into (2)

210 = (15/2) ( 2a₁ -7 - a₁ )

210 ( 2 / 15) =  a₁ - 7

28  = a₁ -  7     

a₁   = 35

And

14d  = -7 - 35   →    14d  = - 42   →   d  = -42/14  =  -3

a₁   = 35      a₂  =   32    a₃  = 29

 x^2 + y^2=169   (1)

5x+12y=169     (2)

The slope of any tangent line to the circle will be  =  -x /y

The slope of the line  =   -5/12

Equating slopes, we have

-x /y  = -5/12    →  y = 12/5 x       sub this into (1)  

x^2 +[ (12/5)x]^2  = 169

x^2 + (144/ 25)x^2  = 169

169x^2 / 25  = 169

x ^2 / 25   = 1

x^2  =25

x =  ± 5

When x = 5, y= (12/5) *5   = 12

When x  = -5, y  = (12/5) * -5  = - 12

Only   (5,12)   will  saitsfy  5x+12y=169

Here's a graph :

x =

The distance traveled  =   pi * diameter   =

 pi * 135m  ≈ 424.12 m

This is easy

Add

1/6 + 1/7 =   13/42

Take the reciprocal  =

42/13 hrs  ≈  3.23  hrs  working together

Let A = number of humans   and B = number of horses

And we know

A + B  = 74       →   B  = 74 - A   (1)

2A + 4B = 196      (2)

Sub (1) into (2)

2A + 4(74 - A)  = 196   simplify

2A + 296 - 4 A  = 196

-2A + 296 =  196     subtract 296 from both sides

-2A  =  -100        divide both sides by  - 2

A  =  50   = humans

74  - 50  = 24  = horses

6.  -<4~/=<1, <3~/=<2

     -AA similarity postulate

     -BA/CB=DE/CD

2. -Def. of angle bisector

5. -<ADB~/=<CDF

Unsure about 9

5. Angle-Angle Similarity Postulate

    proportional 

    segment addition postulate

6. Need a diagram because I'm unsure about the positioning  of angles 1,2,3, and 4